Exam 2019 1B

[Iris]

Hi, I have a question about exam question 1B.

I am a bit confused, because I thought that if we have a lattice containing 1 kind of atom would have a basis (0,0,0). Also in the book I saw the following:

Yet in the solutions, they formulate a basis with more than point (0,0,0). This also influences the structure vector. I see in the lecture notes that this is necessary for an FCC lattice, but in another exam question of 2018:

For some reason the basis is not defined with all the other points of A, only (0,0,0) for A and (1/4,1/4,1/4) for B. When should we make a more “extensive” basis?

[anton-akhmerov]

@Iris

I am a bit confused, because I thought that if we have a lattice containing 1 kind of atom would have a basis (0,0,0).

This is correct if we are considering a primitive unit cell. The problem, however, asks to write the basis using the conventional unit cell.

In the other problem, the primitive lattice vectors are considered. If we used the conventional lattice vectors, we’d have 8 atoms in the basis.